# 2. How many months will it take to pay off a \$9,000 loan with monthly payments of \$225? The APR is 18%.

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1 Lesson 1: The Time Value of Money Study Questions 1. Your mother, who gave you life (and therefore everything), has encouraged you to borrow \$65,000 in student loans. The interest rate is a record-low 2.8% APR, and the repayment calls for 10 years of monthly payments. The first payment is at the end of the first month. How big will your payments be? Get in 12 payments per year. N = 120 = 10 years 12 payments per year I/YR = 2.8% PV = \$65,000 Solve for PMT = \$ How many months will it take to pay off a \$9,000 loan with monthly payments of \$225? The APR is 18%. Get in 12 payments per year. I/YR = 18% PV = \$9,000 PMT = \$225; Solve for N = It will take 62 months to repay the loan. By the way, if you re an A+ student, you should be able to see that your last payment would be only \$ One way to see that is to solve for FV with N = 61; I/YR = 18%; PV = \$9,000; PMT = \$225. Solve for FV = \$ \$ is the loan balance at the end of month 61. The payment at the end of month 62 that gets you out of debt is \$122.60: N = 1; I/YR = 18%; PV = \$120.79; PMT = \$0. Solve for FV = \$ Alternatively, N = 1; I/YR = 18%; PV = \$120.79; FV = \$0. Solve for PMT = \$ You have just won \$5,000 playing the lottery. You are going to save this for your retirement in 30 years. If your investment yields 12%, how much will you have saved for your retirement? Get in 1 payment per year. N = 30; I/YR = 12%; PV = \$5,000; PMT = \$0. Solve for FV = \$149, The business about the lottery is just distracter information.

2 4. You have just inked the deal on a 15-year fixed rate mortgage at 6.5%, financing \$100,000 and obligating yourself to 180 monthly payments of \$ If you pay an extra \$100 per month, in how many months will your house be paid for? Start with the base case: 12 payments per year; PV = \$100,000; N = 180; I/YR = 6.5; PMT = Now set PMT = and solve for N = You have just graduated with \$90,000 of student loans. The terms of the loan call for monthly repayment over 10 years. The interest rate is 5%. What is the amount of your monthly payment? N= 120 = 10 years 12 payments per year I/Y = 5 PV = \$90,000 PMT = \$ You are considering loaning your brother-in-law \$12,000. He has agreed to a monthly repayment schedule lasting 5 years, with the first payment due in one month. If your interest rate is 9%, what is the amount of his monthly payment? N = 60 I/Y = 9 PV = 12,000 PMT = You have just signed a lease for a car. You are required to pay \$500 per month for 60 months. Each payment is due at the START of the month. The first payment is due today. If the correct interest rate is 6% APR, what is the correct value of this car? CF0 = \$500 CF1 = \$500 F01 = 59 INT =.5 = 6/12 NPV = \$25, Get in BEGIN mode N = 60 I/Y = 6 PMT = \$500 Solve for PV = \$25, You have saved \$20,000 as a down payment on a \$100,000 house. Mortgage rates at 5.5% APR with monthly compounding. If you finance for 15 years, what will be the amount of your monthly payment? N = 180 I/Y = 5.5

3 PV = 80,000 PMT = You have incurred \$45,000 in student loans, to be repaid monthly for 10 years at 5% APR. Your intention is to pay an extra \$50 per month each month. How many months will it take until you are out of debt? N = 120 I/Y = 5 PV = \$45,000 PMT = \$ PMT = \$ I/Y = 5 PV = \$45,000 N = months or 14 months early 10. What rate of return is offered by an investment that costs \$5,000 today, pays \$2,000 per year for three years and then requires shut-down expense of \$500 in the fourth year? Use the cash flow menu CF0 = \$5,000 CF1 = \$2,000 F01 = 3 CF2 = = \$500 Compute IRR = 5.41% You could also use the time value of money keys, but it s a bit harde N = 4 PV = \$5,000 PMT = \$2,000 FV = \$2,500 Solve for I/YR = 5.41% 11. What rate of return is offered by an investment that costs \$5,000 today and pays \$2,000 per year at the end of each year, for three years? Use the cash flow menu CF0 = \$5,000 CF1 = \$2,000 F01 = 3 Compute IRR = 9.70% You could also use the time value of money keys: N = 3 PV = \$5,000 PMT = \$2,000 Solve for I/YR = 9.70% 12. What rate of return is offered by a retirement plan where you invest \$2,000 per year for the next 10 years (the first payment is due today) and receive \$250,000 in one payment 30 years from today? Use the cash flow menu. CF0 = \$2,000 CF1 = \$2,000 F01 = 9 CF2 = 0

4 F02 = 20 CF3 = \$250,000 Compute IRR = 10.24% 13. What is the effective annual interest rate of a credit card that has a nominal rate of 24% and monthly compounding? Enter the ICONV menu; set C/Y = 12; NOM = 24% and compute EFF = 26.82% 14. What is the effective annual interest rate of a credit card that has a nominal rate of 12.5% and monthly compounding? Enter the ICONV menu; set C/Y = 12; NOM = 12.5% and compute EFF = 13.24% 15. What is the effective annual interest rate on the following offer: When you buy \$1,000 worth of lumber at Boone County Lumber, the terms are 3 10 net thirty, which means that you can have a 3% discount for paying within 10 days, but no matter what, the bill must be settled within 30 days net thirty represents an offer of a 20-day loan of \$970. To see this, draw a timeline. Day 0 Day 10 Day 20 Day 30 Get lumber; walk out without paying. Pay \$970 (3% discount if paid by day 10). or Pay \$1,000. Pay by day 30 no matter what. Get in 365 payments per year. N = 20; PV = 970; FV = 1,000; compute I/Y = 55.63%. Enter the ICONV menu; set C/Y = 365; NOM = 55.63% and compute EFF = 74.35% Notice that the problem asked for an effective rate, not an APR. 16. Three years ago, you bought a Mini Cooper, financing the \$30,000 purchase price for 5 years with a 7% APR loan and monthly payments. You have just made you 36th payment and are considering the purchase of a Chrysler PT Cruiser. How much do you owe on your loan? Round your answer to the nearest dollar. N = 60 I/Y = 7 PV = 30,000 PMT = AMORT P1 = 1 P2 = 36 BAL = 13,267.70

5 17. You are considering the purchase of a Mini Cooper. The dealer offers you a 36-month 7% APR loan with NO payments for 6 months. The first payment is due 6 months from today. THE LAST PAYMENT IS AT THE END OF THE MONTH 36 MONTHS FROM TODAY. Thus there are 30 payments. Payments are calculated on a \$28,000 principal. The car is worth \$28,000. How big should the payment be? Step one N = 5 I/Y = 7 PV = 28,000 PMT = 0 CPT FV = 28, Step two N = 30 I/Y = 7 PV = 28, PMT = 1, Check: CF0 = 0 CF01 = 0; F01 = 5 CF02 = 1,050.20; F02 = 30 I = 7/12 CPT NPV = 28, You have \$50,000 in student loans: \$20,000 is financed at 5% APR with monthly payments over 10 years; \$30,000 is financed at 24% APR with monthly payments over 10 years. What is the interest rate on your portfolio of debt? Take the sum of the payments on the two loans: \$ = \$ \$ With PV = \$50,000 solve for I/Y = 17.14%. A common mistake would be 19. You are considering refinancing your house. Exactly 10 years ago, you borrowed \$150,000 at 9% APR, agreeing to make 360 monthly payments. You have just made your 120th payment. Interest rates have dropped from 9% to 6%. You want to refinance with a 20-year loan at 6%. By how much would your monthly payment decline? First, we need to figure the balance on the old loan: N = 360 I/Y = 9 PV = \$150,000 PMT = \$1, AMORT P1 = 1 P2 = 120 BAL = \$134, Next, we need to figure the payment on the new loan: N = 240 = 20 years 12 payments per year I/Y = 6 PV = \$134, PMT = \$ Monthly savings = \$ = \$1, \$961.06

6 Hard problem. Hard like a rock. 20. Suppose you graduated last May and began repayment on \$25,000 of student debt financed over 10 years at 3% APR with a payment of \$ on the last day of May. When you do your taxes next April, how much interest will you be able to deduct? N = 120 I/Y = 3 PV = \$25,000 PMT = \$ AMORT P1 = 1 P2 = 8 (When you pay taxes in April, it will be on income and expenses of the prior year.) INT = \$487.40

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